We propose to fuse two main enabling features in cognitive radio systems (CRS): spectrum sensing and location awareness in a single compressed sensing based formalism. In this way, we exploit sparse characteristics of primary units to be detected, both in terms of spectrum used and location occupied. The compressed sensing approach also allows to overcome hardware limitations, in terms of the incapacity to acquire measurements and signals at the Nyquist rate when the spectrum to be scanned is large. Simulation results for realistic network topologies and different compressed sensing reconstruction algorithms testify to the performance and the feasibility of the proposed technique to enable in a single formalism the two main features of cognitive sensor networks. 1. Introduction Cognitive radio (CR) is a smart wireless communication concept that is able to promote the efficiency of the spectrum usage by exploiting the free frequency bands in the spectrum, namely, spectrum holes [1, 2]. Detection of spectrum holes, namely, spectrum sensing, is the first step towards implementing a cognitive radio system. The major problem for spectrum sensing arises in wideband radio, when the radio is not able to acquire signals at the Nyquist sampling rate due to the current limitations in Analog-to-Digital Converter (ADC) technology [3]. Compressive sensing makes it possible to reconstruct a sparse signal by taking less samples than Nyquist sampling, and thus wideband spectrum sensing is doable by compressed sensing (CS). A sparse signal or a compressible signal is a signal that is essentially dependent on a number of degrees of freedom which is smaller than the dimension of the signal sampled at Nyquist rate. In general, signals of practical interest may be only nearly sparse [3]. And typically signals in open networks are sparse in the frequency domain since depending on location, and at some times the percentage of spectrum occupancy is low due to the idle radios [1, 4]. In CS, a signal with a sparse representation in some basis can be recovered from a small set of nonadaptive linear measurements [5]. A sensing matrix takes few measurements of the signal, and the original signal can be reconstructed from the incomplete and contaminated observations accurately and sometimes exactly by solving a simple convex optimization problem [3, 6]. In [7, 8], conditions on this sensing matrix are introduced which are sufficient in order to recover the original signal stably. And remarkably, a random matrix fulfills the conditions with high probability and performs an effective
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